Abstract. The category of filter spaces being isomorphic to the category of grill-determined nearness spaces has become significant in the later part of the twentieth century. During that period, a substantial completion theory has been developed using the equivalence classes of filters in a filter space. However, that completion was quite general in nature, and did not allow the finest such completion. As a result, a completion functor could not be defined on . In this paper, this issue is partially addressed by constructing a completion that is finer than the existing completions. Also, a completion functor is defined on a subcategory of comprising all filter spaces as objects.

Received: August 16, 2015

AMS Subject Classification: 54D35, 54A20, 54C20

Key Words and Phrases: filter space, Cauchy map, convergence structure, -map, stable completion, completion in standard form

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